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Mechanical Properties Of Fluids

Question
CBSEENPH11018487

A plate of area 20x10 cm2 is placed over the honey poured on the table. The layer of honey between plate and the table is 2.5mm thick. To move the plate with velocity 3 cm/s a horizontal force of 30720 dyne is required. Find the coefficient of viscosity of honey.

Solution

The formula for viscous force is given by,
straight F space equals space straight eta space straight A dv over dx

rightwards double arrow space straight eta space equals space straight F over straight A dx over dv space space space space... thin space left parenthesis 1 right parenthesis thin space
Here given that,
Horizontal force, F = 30720 dyne    
Area of the plate, A = 200 cm
Velocity with which the plate is moved = 3 cm/sec
Thickness of the layer of honey between the plate and table = 2.5 mm 
Putting the values in equation (1), we get
dv over dx space equals space fraction numerator 3 over denominator 0.25 end fraction space equals space 12 space straight s to the power of negative 1 end exponent space

Therefore comma space

straight eta space equals space 30720 over 200 cross times 1 over 12 space equals space 12.8 space poise
is the required coefficient of viscosity of honey.